Yer only have to go back to Plank to find a pretty detailed argument that there are three fundamental dimensional constants from which all others can be derived. They are length, time and mass. Plank argues that as long as you got a tape measure, a clock and set of scales you can measure anything in the universe.
Seems reasonable but various philosophers have argued over the details sayin’ maybe there are no constants or perhaps two or God knows how many. But being philosphers, they ain’t interested in actually provin’ anything only arguin’ about it.
Now a group of Brazilian eggheads this week say they have proven the result objectively and that Plank is wrong. They reckon there are only two of fundamental dimensional constants and that these correspond to length and time. They argue that all ya need is a tape measure and a clock.
A key to their thinkin is that they assume that all that can be measured are intervals in space and time. This leads to the idea that gravitational mass is the same as inertial mass, which is a big leap but one they say they prove. Given that, mass is simply the acceleration produced on a test particle at a certain distance. Ya don’t need no scales to measure that.
Interesting approach. When it comes to fundamental dimensional constants, two is a big improvement on three.
Ref: arxiv.org/abs/0711.4276: The Number of Dimensional Fundamental Constants
They say “dimensional”, not “dimensionless”, and indeed c, G and h are dimensional constants (AFAIK).
Much obliged, DR. What on Earth was ah thinkin’!